# Thread: bottle cup and container problem

1. ## bottle cup and container problem

Dear Sir,

I need some help to know the solution of the below question.

Thanks
Kingman

John used 2/5 of a bottle of water to fill some cups and 5/9 of the remaining water to fill 4 containers.
The capacity of each container was 5 times that of a cup. How many cups did he fill with water?

2. Hi kingman,
What have you tried? Let x = liters in bottle ( any units will do ). Express each operation in terms of x.You can write a simple equation in x. Try it

bjh

3. ok lets say u have Y units of water. so (5/9)Y = 4C where C = the capacity of the containers. Now the question tells u that C = 5D (D = capacity of the cups)

After defining all the terms, this should be a simple substitution problem where if C = 5D then (5/9) = 4 (5D) = 20D
Therefore (1/9) = 4D (20/5 = 4)
so 1/9 of the total water you have fills up 4 cups, therefore 2/9 fills up 8 cups

Thank me for doing your homework ^^

4. Thanks very much for the help but the answer is 24!

5. That's because holaboo misunderstood the problem. He is assuming that 5/9 of the whole bottle will fill 4 containers when it is said that 5/9 of the remaining water will fill 4 containers. If you use 2/5 of the bottle to fill the cups then there is 1- 2/5= 3/5 of the bottle remaining. 5/9 of 3/5= 3/9= 1/3 of the water in the bottle. That fills 4 containers which is the same as 20 cups. If 1/3 of the water fills 20 cups, how many cups will 2/5 fill? That's a fairly simple proportion. Set up as an equality of fractions, $\displaystyle \frac{20}{\frac{1}{3}}= \frac{x}{\frac{2}{5}}$, and solve for x.